From: Jim Pryor <profjim@jimpryor.net>
Date: Tue, 2 Nov 2010 15:56:08 +0000 (-0400)
Subject: cat theory tweaks
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=c0a6070f7c11da38419b5e5da90afeddc6520b95

cat theory tweaks

Signed-off-by: Jim Pryor <profjim@jimpryor.net>
---

diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 402a5e77..588d1a30 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -404,16 +404,15 @@ Finally, we substitute <code>((join G') -v- (M &gamma;) -v- &phi;)</code> for <c
 	        ((join R') (M ((join R') (M &rho;) &gamma;)) &phi;) = ((join R') (M &rho;) (join G') (M &gamma;) &phi;)
     
 			which by the distributivity of functors over composition, and helping ourselves to associativity on the lhs, yields:
-	       ((join R') (M join R') (MM &rho;) (M &gamma;) &phi;) = ((join R') (M &rho;) (join G') (M &gamma;) &phi;)
+	        ((join R') (M join R') (MM &rho;) (M &gamma;) &phi;) = ((join R') (M &rho;) (join G') (M &gamma;) &phi;)
   
 			which by lemma 1, with &rho; a transformation from G' to MR', yields:
-	       ((join R') (M join R') (MM &rho;) (M &gamma;) &phi;) = ((join R') (join MR') (MM &rho;) (M &gamma;) &phi;)
+	        ((join R') (M join R') (MM &rho;) (M &gamma;) &phi;) = ((join R') (join MR') (MM &rho;) (M &gamma;) &phi;)
 
-			which will be true for all &rho;,&gamma;,&phi; just in case:
+			which will be true for all &rho;,&gamma;,&phi; only when:
 	        ((join R') (M join R')) = ((join R') (join MR')), for any R'.
 
-			which will in turn be true just in case:
-
+			which will in turn be true when:
       (ii') (join (M join)) = (join (join M))